M40-50

Question

A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale, in centimeters, that he uses when measuring 1 meter of cloth? (1 meter = 100 centimeters)

A. 70
B. 72
C. 75
D. 76
E. 77

Show Answer

Official Answer

D

A. 70
B. 72
C. 75
D. 76
E. 77

Bunuel · Answer

Official Solution:

A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale, in centimeters, that he uses when measuring 1 meter of cloth? (1 meter = 100 centimeters)

A. 70
B. 72
C. 75
D. 76
E. 77

Show Answer

Official Answer

D

A. 70
B. 72
C. 75
D. 76
E. 77

Let's assume that the cost of 1 centimeter of cloth is $1. Therefore, for a meter (100 centimeters), the base cost would be $100. However, the merchant claims to sell 1 meter of cloth at a 5% loss, which means he is selling it for $95 (95% of the original cost). 
 
In reality, this $95 still incorporates a 25% gain for the merchant, which means  1.25 * ($1 * 	ext{actual length in meters}) = $95 . This yields  	ext{actual length in meters} = 0.76 . So, the actual length of cloth the merchant claims to be 1 meter is, in fact, only 0.76 meters.

Answer: D

PReciSioN · Answer

I feel that probably the measure of (false) scale that he is using to measure out 100 metres (in front of customers) should be greater than 100 metres. and should be 100/76 = 131 metres.

Bunuel · Answer

The  actual  length of cloth he gives for  false  1 meter should be less than 100 centimeters. Therefore, the solution is correct: the measure of the  false  scale for 1 meter is  real  76 centimeters. So, what he claims to be 1 meter is in reality only 76 centimeters.

pinkman27 · Answer

Let CP be $100 for 1 m($1 per 1 cm)
Therefore
SP is $95 for 1m(Shopkeeper has a loss of 5%)

But the shopkeeper gains 25%

Therefore
His actual CP(Y) is given by

95-Y  = 0.25
 Y

Y= 76

This gives us basically the measure of the scale.

an1995 · Answer

Hi  Bunuel , can you please post similar questions such as this? Approaching these Qs has been very tricky for a while now!

Bunuel · Answer

Check  Tricky Trades: The Dishonest Merchants and Falsified Scales  from out  Special Questions Directory .

markiv2024 · Answer

Bunuel   bb  Since it is not given if the loss is monetary or material, I assumed the loss of 5% to be material loss. The merchant says he sells 105m for the price of 100m. But in reality he gains 25% as in he only sells 75m of cloth. Now my solution comes to 71.4. I chose 72. I wonder what's wrong with this approach. Infact the whole 'measure of scale' thing suggests this approach, aint it?

Bunuel · Answer

I don't think so. The loss is in money, not in material. It’s a merchant; he buys and sells for money, so losses and gains are always monetary.

Dream009 · Answer

See - Let cost be 100 for 100 quantity 
now he says he sells 100 at 95 ----- making a loss of 5 - but that's not true ---- He is selling some Q such that
Q*5/4 = 95
and 5/4 is 1.25
So Q= 95*4/5 = 76 Answer.

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